Wozniacki wins through in New Haven
The former world number one seemed on course to lose the opening set after falling behind in the tie-break, but she managed to pull through and take it under pressure.
Wozniacki did not give her Swedish opponent a glimmer of an opportunity to get back into the match in the second set as she broke with ease to take it for the loss of just two games.
Cibulkova, like Wozniacki, had to battle through a tough opening set before managing to take the second in convincing fashion against the German.
Safarova booked her place in the quarters with a comprehensive 6-4 6-0 victory over China’s Zheng Jie.